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Updated: May 17, 2025
A pair of shoes, perhaps, was never yet wrought to the highest degree of perfection that commodity is capable of attaining; yet it is necessary, at least very useful, that there should be some politicians and moralists, even some geometers, poets and philosophers, among mankind.
Establishing the relation between these elements and their primitives, the way lay open to the Integral Calculus. The greatest geometers of the day, Pascal, Roberval, and others, unhesitatingly adopted this method, and employed it in the abstruse researches which engaged their attention.
Even in the branch of paleontology, or the study of the fossil remains of extinct animals, it would be impracticable to give the names of those who have added so much to our knowledge of the earth and its inhabitants in the ages that preceded man. ASTRONOMY. The great French geometers, Lagrange and Laplace, made an epoch in astronomical science.
This generality increased tenfold the difficulties of the problem; neither Clairaut nor D'Alembert was, however, arrested by them. Thanks to the efforts of these two eminent geometers, thanks to some essential developments due to their immediate successors, and especially to the illustrious Legendre, the theoretical determination of the figure of the earth has attained all desirable perfection.
A certain Chever also performed sundry singular mathematical feats, such as squaring the circle, a problem which he reduced to the single question, Construere mundum divinae menti analogum, and showing that the parabola, the only conic section squared by ancient or modern geometers, could never be quadrated, to the eternal discomfiture and discredit of the shade of Archimedes.
But geometers are men; and the contagion of patriotic fervour which swept over Germany after the battle of Leipsic did not spare Gauss's promising pupil. He took up arms in the Hanseatic Legion, and marched and fought until the oppressor of his country was safely ensconced behind the ocean-walls of St. Helena.
I have now arrived at the conclusion of the task which I had imposed upon myself. I shall be pardoned for having given so detailed an exposition of the principal discoveries for which philosophy, astronomy, and navigation are indebted to our geometers. It has appeared to me that in thus tracing the glorious past I have shown our contemporaries the full extent of their duty towards the country.
“In geometry the principles are palpable, but removed from common use. . . . In the sphere of natural wit or acuteness, the principles are in common use and before all eyes—it is only a question of having a good view of them; for they are so subtle and numerous, that some are almost sure to escape observation. . . . All geometers would be men of acuteness if they had sufficient insight, for they never reason falsely on the principles recognised by them.
Each new invention would violate a greater number of known analogies; for if a theory be required to embrace some false principle, it becomes more visionary in proportion as facts are multiplied, as would be the case if geometers were now required to form an astronomical system on the assumption of the immobility of the earth.
"As a coach goes faster when it is empty, a man by fasting can be better united to God; for it is a principle with geometers that a round body can never touch a plane except in one point.... A belly too well filled becomes round, it cannot touch God except in one point; but fasting flattens the belly until it is united with the surface of God at all points."
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